Generate trends / drift in time series¶

In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from badgers.generators.time_series.trends import GlobalAdditiveLinearTrendGenerator, AdditiveLinearTrendGenerator, RandomlySpacedLinearTrends

import numpy as np import pandas as pd import matplotlib.pyplot as plt from badgers.generators.time_series.trends import GlobalAdditiveLinearTrendGenerator, AdditiveLinearTrendGenerator, RandomlySpacedLinearTrends

Setup random generator¶

In [2]:

from numpy.random import default_rng
seed = 0
rng = default_rng(seed)

from numpy.random import default_rng seed = 0 rng = default_rng(seed)

Generate data (gaussian white noise)¶

In [3]:

X = pd.DataFrame(data=rng.normal(loc=0, scale=0.1, size=(100, 2)), columns=['dimension_0', 'dimension_1'])

X = pd.DataFrame(data=rng.normal(loc=0, scale=0.1, size=(100, 2)), columns=['dimension_0', 'dimension_1'])

In [4]:

fig, ax = plt.subplots(1, sharex=True, sharey=True, figsize=(6,3))
X.plot(ax=ax);

fig, ax = plt.subplots(1, sharex=True, sharey=True, figsize=(6,3)) X.plot(ax=ax);

Add linear trend¶

In [5]:

generator = GlobalAdditiveLinearTrendGenerator(random_generator=rng)

generator = GlobalAdditiveLinearTrendGenerator(random_generator=rng)

In [6]:

slope = np.array([0.01,-0.02]) # slope: increase per time unit
Xt, _ = generator.generate(X, y=None, slope=slope)

slope = np.array([0.01,-0.02]) # slope: increase per time unit Xt, _ = generator.generate(X, y=None, slope=slope)

In [7]:

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6))
# first plot: original data
X.plot(ax=axes[0])
axes[0].set_title('Original data')

# second plot: transformed data
# visualizing added trends
axes[1].plot([0,len(X)],[0,len(X)*slope[0]], ls='--', linewidth=1, color='red')
axes[1].plot([0,len(X)],[0,len(X)*slope[1]], ls='--', linewidth=1, color='red')
Xt.plot(ax=axes[1])
axes[1].set_title('Transformed data')

plt.tight_layout();

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6)) # first plot: original data X.plot(ax=axes[0]) axes[0].set_title('Original data') # second plot: transformed data # visualizing added trends axes[1].plot([0,len(X)],[0,len(X)*slope[0]], ls='--', linewidth=1, color='red') axes[1].plot([0,len(X)],[0,len(X)*slope[1]], ls='--', linewidth=1, color='red') Xt.plot(ax=axes[1]) axes[1].set_title('Transformed data') plt.tight_layout();

Add linear trend for a specific time interval¶

In [8]:

generator = AdditiveLinearTrendGenerator(random_generator=rng)

generator = AdditiveLinearTrendGenerator(random_generator=rng)

In [9]:

slope = np.array([0.01,-0.02])
start = 25
end = 75
Xt, _ = generator.generate(X, y=None, slope=slope, start=start, end=end)

slope = np.array([0.01,-0.02]) start = 25 end = 75 Xt, _ = generator.generate(X, y=None, slope=slope, start=start, end=end)

In [10]:

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6))
# first plot: original data
X.plot(ax=axes[0])
axes[0].set_title('Original data')

# second plot: transformed data
# visualizing added trends
axes[1].plot([start,end],[Xt.iloc[start,0],Xt.iloc[start,0] + (end-start)*slope[0]], ls='--', linewidth=1, color='red')
axes[1].plot([start,end],[Xt.iloc[start,1],Xt.iloc[start,1] + (end-start)*slope[1]], ls='--', linewidth=1, color='red')
Xt.plot(ax=axes[1])
axes[1].set_title('Transformed data')

plt.tight_layout();

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6)) # first plot: original data X.plot(ax=axes[0]) axes[0].set_title('Original data') # second plot: transformed data # visualizing added trends axes[1].plot([start,end],[Xt.iloc[start,0],Xt.iloc[start,0] + (end-start)*slope[0]], ls='--', linewidth=1, color='red') axes[1].plot([start,end],[Xt.iloc[start,1],Xt.iloc[start,1] + (end-start)*slope[1]], ls='--', linewidth=1, color='red') Xt.plot(ax=axes[1]) axes[1].set_title('Transformed data') plt.tight_layout();

Adding linear trends (of random slopes) in randomly chosen time intervals¶

In [11]:

generator = RandomlySpacedLinearTrends(random_generator=rng)

generator = RandomlySpacedLinearTrends(random_generator=rng)

In [12]:

Xt, _ = generator.generate(X, y=None, n_patterns=5, min_width_pattern=5, max_width_patterns=10, slope_min=-0.1, slope_max=0.1)

Xt, _ = generator.generate(X, y=None, n_patterns=5, min_width_pattern=5, max_width_patterns=10, slope_min=-0.1, slope_max=0.1)

In [13]:

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6))
# first plot: original data
X.plot(ax=axes[0])
axes[0].set_title('Original data')

# second plot: transformed data
Xt.plot(ax=axes[1])
axes[1].set_title('Transformed data')

# show where the patterns are located
bottom = np.min(Xt)
height = np.max(Xt) - np.min(Xt)
for (start, end), slope in zip(generator.patterns_indices_, generator.slopes_):
    # add red rectangle for visualizing the time interval
    width = end-start
    left = start
    rect = plt.Rectangle((left, bottom), width, height,
                         facecolor="red", alpha=0.1)
    axes[1].add_patch(rect)
    # vizualizing trends
    axes[1].plot([start,end],[Xt.iloc[start,0],Xt.iloc[start,0] + (end-start)*slope[0]], ls='--', linewidth=1, color='red')
    axes[1].plot([start,end],[Xt.iloc[start,1],Xt.iloc[start,1] + (end-start)*slope[1]], ls='--', linewidth=1, color='red')

plt.tight_layout();

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6)) # first plot: original data X.plot(ax=axes[0]) axes[0].set_title('Original data') # second plot: transformed data Xt.plot(ax=axes[1]) axes[1].set_title('Transformed data') # show where the patterns are located bottom = np.min(Xt) height = np.max(Xt) - np.min(Xt) for (start, end), slope in zip(generator.patterns_indices_, generator.slopes_): # add red rectangle for visualizing the time interval width = end-start left = start rect = plt.Rectangle((left, bottom), width, height, facecolor="red", alpha=0.1) axes[1].add_patch(rect) # vizualizing trends axes[1].plot([start,end],[Xt.iloc[start,0],Xt.iloc[start,0] + (end-start)*slope[0]], ls='--', linewidth=1, color='red') axes[1].plot([start,end],[Xt.iloc[start,1],Xt.iloc[start,1] + (end-start)*slope[1]], ls='--', linewidth=1, color='red') plt.tight_layout();

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